We use a holographic black hole approach to study the QCD phase diagram at finite temperature and baryon-chemical potential, $\mu_B$.
The free parameters of our black hole model were engineered to mimic the equation of state of QCD obtained on the lattice at zero $\mu_B$. Once the parameters were fixed, the black hole model predicts the equation of state at finite $\mu_B$.
In this contribution, we discuss the mapping of the black hole model in the QCD phase diagram and show that the crossover transition, between hadrons and the quark-gluon plasma, ends in a critical point where a first order line begins.